Q-26

Q-26 O i O Oto

The displacement of the particle can be calculated as follows:
$$\begin{gathered} \overrightarrow{s}=\overrightarrow{b}-\overrightarrow{a}=(7-1)\hat{i}+(10-2)\hat{j}+(5+2)\hat{k} \\ \Rightarrow \overrightarrow{s}=6\hat{i}+8\hat{j}+7\hat{k} \end{gathered}$$

The net force on the particle is
$$\begin{gathered} \overrightarrow{F}={\overrightarrow{F}}_1+{\overrightarrow{F}}_2=(2\hat{i}-3\hat{j}+3\hat{k})+(\hat{i}+\hat{j}-2\hat{k}) \\ \Rightarrow \overrightarrow{F}=3\hat{i}-2\hat{j}+\hat{k} \end{gathered}$$

Then work done will be
$$\begin{gathered} W=\overrightarrow{F}.\overrightarrow{s}=(3\hat{i}-2\hat{j}+\hat{k}).(6\hat{i}+8\hat{j}+7\hat{k})=18-16+7 \\ \Rightarrow W=9 \mathrm{N} \mathrm{m} \end{gathered}$$